1. Field of Invention
This invention is directed to apparatus and methods of actuation allocation of a group of implementation units.
2. Description of Related Art
Smart matter systems are systems with a large number of elements such as sensors, actuators, and/or allocators. A major problem for such systems is to coordinate the actions of many elements in order to obtain a desired result or goal for the entire smart matter system. The desired result is achieved by controlling or allocating a particular action to each individual actuator to obtain a cumulative actuation over all the actuators. The desired individual actuation of each actuator can be achieved in a number of ways. However, the actuation must be accomplished in some optimal or near-optimal way while satisfying a number of constraints.
For systems having a relatively small number of actuators, it is relatively easy to determine the desired individual actuation to obtain an overall system actuation, e.g., using an exhaustive search method. Unfortunately, the number of ways to produce a desired collective result increases exponentially with the number of actuators to be controlled. Thus, the problem of allocating actuation among a number of actuators becomes considerably more difficult as the number of actuators increases in the smart matter regime. Moreover, as the number of actuators increases, the time available to compute the allocation often decreases because of the need to communicate the allocation decision to the increased number of actuators.
A related art method of allocating actuators involves an exhaustive search technique, whereby a systematic search is conducted through all possible actuation allocations that are able to accomplish the desired result.
Another related art method of allocating actuation involves solving a mixed integer nonlinear programming problem. The allocation problem is cast as a mixed integer nonlinear programming problem over a set of continuous and integer variables to select the actuation for each actuator. Various methods, such as branch-and-bound, Bender's decomposition, and outer approximations are used to solve mixed integer nonlinear programming problems. These methods solve the optimization problem without integer constraints and then incrementally enforce the integer constraints. The result is that, rather than computing all of the exponential number of combinations that are possible, only promising branches of the search tree are computed with the expense of solving a nonlinear optimization problem at each node of the tree.
Other related art methods to solve the constrained optimization for the actuator allocation use standard optimization methods such as interior point or active set methods.
However, these related art methods have numerous disadvantages and shortfalls.